DYNAMICS AND CONTROL OF ELASTIC JOINT MANIPULATORS

The investigations presented in this paper are based on our previous s tudies where the modeling and control problems of rigid body manipulat ors were treated through the so-called vector-parametrization of the S O(3) group. The nice property of this parametrization, which also disp lays a Lie group structure, is that it drastically simplifies some con siderations and reduces the computational burden in solving direct kin ematic problems, inverse kinematic problems and dynamic modeling by mo re than 30% in comparison with the methods used hitherto. This stateme nt, which is valid for models built through vector-parameter, becomes stronger in pure vector-parameter considerations. It is proved additio nally that the computational effectiveness of the vector parameter app roach increases with the increasing number of the revolute degrees of freedom. Here we show that this can be used successfully in the proble ms of elastic joint manipulators where, besides the real n links, n fi ctious links are included and an additional n revolute degrees of free dom are involved. The present paper also considers the role of group r epresentations of the rotation motions in the modeling and control of manipulators with elastic joints. Dynamic models 'through' vector-para meter and in 'pure' vector-parameter form are developed and the invers e dynamic problem is discussed. It is shown that the nonlinear equatio ns of motion are globally linearizable by smooth invertible coordinate transformation and nonlinear state feedback.